{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "e966a723",
   "metadata": {},
   "source": [
    "# 1D harmonic oscillator physics-informed neural network (PINN)\n",
    "\n",
    "This notebook contains the code to reproduce the plots presented in my blog post [\"So, what is a physics-informed neural network?\"](https://benmoseley.blog/my-research/so-what-is-a-physics-informed-neural-network/). \n",
    "\n",
    "Please read the post for more details!\n",
    "\n",
    "## Problem overview\n",
    "\n",
    "The example problem we solve here is the 1D damped harmonic oscillator:\n",
    "$$\n",
    "m \\dfrac{d^2 x}{d t^2} + \\mu \\dfrac{d x}{d t} + kx = 0~,\n",
    "$$\n",
    "with the initial conditions\n",
    "$$\n",
    "x(0) = 1~~,~~\\dfrac{d x}{d t} = 0~.\n",
    "$$\n",
    "We will focus on solving the problem for the under-damped state, i.e. when \n",
    "$$\n",
    "\\delta < \\omega_0~,~~~~~\\mathrm{with}~~\\delta = \\dfrac{\\mu}{2m}~,~\\omega_0 = \\sqrt{\\dfrac{k}{m}}~.\n",
    "$$\n",
    "This has the following exact solution:\n",
    "$$\n",
    "x(t) = e^{-\\delta t}(2 A \\cos(\\phi + \\omega t))~,~~~~~\\mathrm{with}~~\\omega=\\sqrt{\\omega_0^2 - \\delta^2}~.\n",
    "$$\n",
    "\n",
    "This problem was inspired by the following blog post: https://beltoforion.de/en/harmonic_oscillator/.\n",
    "\n",
    "## Workflow overview\n",
    "\n",
    ">First we will train a standard neural network to interpolate a small part of the solution, using some observed training points from the solution.\n",
    "\n",
    ">Next, we will train a PINN to extrapolate the full solution outside of these training points by penalising the underlying differential equation in its loss function.\n",
    "\n",
    "\n",
    "## Environment set up\n",
    "\n",
    "We train the PINN using PyTorch, using the following environment set up:\n",
    "```bash\n",
    "\n",
    "conda create -n pinn python=3\n",
    "conda activate pinn\n",
    "conda install jupyter numpy matplotlib\n",
    "conda install pytorch torchvision torchaudio -c pytorch\n",
    "```\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "0e3d0d5d",
   "metadata": {},
   "outputs": [],
   "source": [
    "from PIL import Image\n",
    "\n",
    "import numpy as np\n",
    "import torch\n",
    "import torch.nn as nn\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "2ac19c5e",
   "metadata": {},
   "outputs": [],
   "source": [
    "def save_gif_PIL(outfile, files, fps=5, loop=0):\n",
    "    \"Helper function for saving GIFs\"\n",
    "    imgs = [Image.open(file) for file in files]\n",
    "    imgs[0].save(fp=outfile, format='GIF', append_images=imgs[1:], save_all=True, duration=int(1000/fps), loop=loop)\n",
    "    \n",
    "def oscillator(d, w0, x):\n",
    "    \"\"\"Defines the analytical solution to the 1D underdamped harmonic oscillator problem. \n",
    "    Equations taken from: https://beltoforion.de/en/harmonic_oscillator/\"\"\"\n",
    "    assert d < w0\n",
    "    w = np.sqrt(w0**2-d**2)\n",
    "    phi = np.arctan(-d/w)\n",
    "    A = 1/(2*np.cos(phi))\n",
    "    cos = torch.cos(phi+w*x)\n",
    "    sin = torch.sin(phi+w*x)\n",
    "    exp = torch.exp(-d*x)\n",
    "    y  = exp*2*A*cos\n",
    "    return y\n",
    "\n",
    "class FCN(nn.Module):\n",
    "    \"Defines a connected network\"\n",
    "    \n",
    "    def __init__(self, N_INPUT, N_OUTPUT, N_HIDDEN, N_LAYERS):\n",
    "        super().__init__()\n",
    "        activation = nn.Tanh\n",
    "        self.fcs = nn.Sequential(*[\n",
    "                        nn.Linear(N_INPUT, N_HIDDEN),\n",
    "                        activation()])\n",
    "        self.fch = nn.Sequential(*[\n",
    "                        nn.Sequential(*[\n",
    "                            nn.Linear(N_HIDDEN, N_HIDDEN),\n",
    "                            activation()]) for _ in range(N_LAYERS-1)])\n",
    "        self.fce = nn.Linear(N_HIDDEN, N_OUTPUT)\n",
    "        \n",
    "    def forward(self, x):\n",
    "        x = self.fcs(x)\n",
    "        x = self.fch(x)\n",
    "        x = self.fce(x)\n",
    "        return x"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "80ee01e6",
   "metadata": {},
   "source": [
    "## Generate training data\n",
    "\n",
    "> First, we generate some training data from a small part of the true analytical solution.\n",
    "\n",
    "For this problem, we use $\\delta=2$, $\\omega_0=20$, and try to learn the solution over the domain $x\\in [0,1]$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "474e8445",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "torch.Size([500, 1]) torch.Size([500, 1])\n",
      "torch.Size([10, 1]) torch.Size([10, 1])\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "d, w0 = 2, 20\n",
    "\n",
    "# get the analytical solution over the full domain\n",
    "x = torch.linspace(0,1,500).view(-1,1)\n",
    "y = oscillator(d, w0, x).view(-1,1)\n",
    "print(x.shape, y.shape)\n",
    "\n",
    "# slice out a small number of points from the LHS of the domain\n",
    "x_data = x[0:200:20]\n",
    "y_data = y[0:200:20]\n",
    "print(x_data.shape, y_data.shape)\n",
    "\n",
    "plt.figure()\n",
    "plt.plot(x, y, label=\"Exact solution\")\n",
    "plt.scatter(x_data, y_data, color=\"tab:orange\", label=\"Training data\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2d8cd505",
   "metadata": {},
   "source": [
    "## Normal neural network\n",
    "\n",
    "> Next, we train a standard neural network (fully connected network) to fit these training points.\n",
    "\n",
    ">We find that the network is able to fit the solution very closely in the vicinity of the training points, but does not learn an accurate solution outside of them."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "7847195e",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def plot_result(x,y,x_data,y_data,yh,xp=None):\n",
    "    \"Pretty plot training results\"\n",
    "    plt.figure(figsize=(8,4))\n",
    "    plt.plot(x,y, color=\"grey\", linewidth=2, alpha=0.8, label=\"Exact solution\")\n",
    "    plt.plot(x,yh, color=\"tab:blue\", linewidth=4, alpha=0.8, label=\"Neural network prediction\")\n",
    "    plt.scatter(x_data, y_data, s=60, color=\"tab:orange\", alpha=0.4, label='Training data')\n",
    "    if xp is not None:\n",
    "        plt.scatter(xp, -0*torch.ones_like(xp), s=60, color=\"tab:green\", alpha=0.4, \n",
    "                    label='Physics loss training locations')\n",
    "    l = plt.legend(loc=(1.01,0.34), frameon=False, fontsize=\"large\")\n",
    "    plt.setp(l.get_texts(), color=\"k\")\n",
    "    plt.xlim(-0.05, 1.05)\n",
    "    plt.ylim(-1.1, 1.1)\n",
    "    plt.text(1.065,0.7,\"Training step: %i\"%(i+1),fontsize=\"xx-large\",color=\"k\")\n",
    "    plt.axis(\"off\")\n",
    "    \n",
    "    \n",
    "# train standard neural network to fit training data\n",
    "torch.manual_seed(123)\n",
    "model = FCN(1,1,32,3)\n",
    "optimizer = torch.optim.Adam(model.parameters(),lr=1e-3)\n",
    "files = []\n",
    "for i in range(1000):\n",
    "    optimizer.zero_grad()\n",
    "    yh = model(x_data)\n",
    "    loss = torch.mean((yh-y_data)**2)# use mean squared error\n",
    "    loss.backward()\n",
    "    optimizer.step()\n",
    "    \n",
    "    \n",
    "    # plot the result as training progresses\n",
    "    if (i+1) % 10 == 0: \n",
    "        \n",
    "        yh = model(x).detach()\n",
    "        \n",
    "        plot_result(x,y,x_data,y_data,yh)\n",
    "        \n",
    "        file = \"plots/nn_%.8i.png\"%(i+1)\n",
    "        plt.savefig(file, bbox_inches='tight', pad_inches=0.1, dpi=100, facecolor=\"white\")\n",
    "        files.append(file)\n",
    "    \n",
    "        if (i+1) % 500 == 0: plt.show()\n",
    "        else: plt.close(\"all\")\n",
    "            \n",
    "save_gif_PIL(\"nn.gif\", files, fps=20, loop=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "285d57ca",
   "metadata": {},
   "source": [
    "## PINN\n",
    "\n",
    "> Finally, we add the underlying differential equation (\"physics loss\") to the loss function. \n",
    "\n",
    "The physics loss aims to ensure that the learned solution is consistent with the underlying differential equation. This is done by penalising the residual of the differential equation over a set of locations sampled from the domain.\n",
    "\n",
    "Here we evaluate the physics loss at 30 points uniformly spaced over the problem domain $([0,1])$. We can calculate the derivatives of the network solution with respect to its input variable at these points using `pytorch`'s autodifferentiation features, and can then easily compute the residual of the differential equation using these quantities."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "4cc42d96",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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NyhhjjDHGjJZYtQPYQneW8A5pAnzCFkEPAP5U7aDMJszrEGAWcAAwCVgB3AEssBXVjDHGGDNUddcDG5kf4pVDpCjgxQgPSabzfrWDMhvhktejgA8C06Ot06Ovj4r2G2OMMcZsUr32wD4BrC2r15mQYIJPOLmEvytu6TtTQ7LZrAfsOoP/O2gHFh8b4C+ezMpgN55Y00ixB1gFHAw8DjxZ1WCNMcYYUxfqMoEt5FJhMp2/s4Q3LUEwIS5BS6/GD8AS2JqRzWabgJND5YRV2pxcEu488TZ2SQiU26Q3mCwH906XJfe9lnvumMmidbj5fC2BNcYYY8wm1WUCG5lfxj8CSvhos0f4OuC31Q7KQDabPWhd2JB9Ipi48+KgvaNILExQFCAESSjEfZgwxZs18W5/p9cc7N1/25Hc0NdQ7cCNMcYYUxdEtT7HziTT+e2By9qkN+mjTd0af6pIbN9CLtVX7di2Vtls1iuq95FHylO+/FQwfmIZr7dH48vKeN0TWD8hQTlRxiu7oyWm4rWANE/x1pVe7z/5cOA3pzKZzPLq3oUxxhhjal29DuICeA5YUla3KpdP2AHsXd2Qtl7ZbNZbETaffWNx1jcXBhMm9mj8+fXa8FQZvxuELhq7PMKKgXZaFg3WigYrl4etsctKc171eHnS1dlsdsfq3YUxxhhj6kHdJrCFXEqB+SW8boCYhM24OkozyrLZrDwdjPvuf0vTP96piUSXJp7pJb4SXphYYF0f8WumyfJ/7ec9vniCrO/2UC9GGEtQkqJ6z/UR636oPGXXu0vTrvrqvG9YEmuMMcaYDarnGliA+WW8EwD10UaP8EDgp1WOaauzoDzh9IfKUz5UxpNuTSwq4RaZAJ4HfgZcU8gdU2LeyQLMClT2/2f4un1+XU7NeVKnTekj3oeyplWKOzwTjNu+V2PXfiFzzoHfyX55afXuyhhjjDG1qm5rYAGS6fwE4JpW6ZsRI2zu0viiErH9C7nUumrHtrV499d+dsIT5UkXlPBj3Rp/rkis/7X/F3BOIZfq3FDbZDovwHHA6UATqLRKcXqMsHmy17Vw99iyA36U/WL3KNyGMcYYY+pI3ZYQABRyqVXAk4F6XQAxwhZg3+pGtfU46Ws/32FhMOHcEn6sT2MrKpLX3wJnbCx5BVcGUsil/oFbzGA5iHZp4tkQKS4PW3Z8pLzN5dls1hY4MMYYY8xL1HUCG7E62Co44Yxfy3NB+997Nd5axuvuIdY/e8DvCrnUz6Ma5SEp5FKPAx8AligSdGpikUL4fNj6utuK03MjcgPGGGOMqVtjIYG9s4zXw4t1sK+vdkBbg/Wa+OY6bdxNIezW+HPRgK0rcDWvm62QSy0BPgYsD/GKPRpfArAsbP34m756wZHDFrgxxhhj6t5YSGDvBgmiJBafcJdkOr9NtYMac+Z1CPM6ZjOv4+Rbzjz4m+vDxKcFlV6NLw3d3K6P4mpet7ioupBLPQt8FugtEltXxF8D4q0JG3+155f/2jZMd2KMMcaYOlf3CWwhl+oGHgw0KiOwOtjhN69DgKOAD5bVm5Erv+eUEInHKdFIL6DdwBeHYxGJQi71KHAmQI/Gl4VIqYw/sVlKF0eDvowxxhizlav7BDZyV4loIJerg7UEdnjNAg4GCmcHp+y6VMdNUURDZVULva2vkcd+X8ilFg/XxQq51PXApYqEPRpfCtCrscMnSefc4bqGMcYYY+rXWElg7x5QB3tAtQMaYw4A1i0KJzdcHeyfcpu0G7Sc9JYu/GPiG+tH4Jo/Ah4v4XeW8NcKSAn/rNnpyyeNwLWMMcYYU0fGSgJ7P0ipog52J6uDHVaTgO5sMPeYPuKtgIqG633C4EuxP17ti04e7gsWcqki8BWgt1vjyxQCgXFt0vfj4b6WMcaY6hMRFZHZW9j2YBF5bLhjMrVrTCSwhVyqB3hoQB3sftWNakxZ8WA4fcp94azXAghhF2h4iH//rXt7C8vA8k203yKFXKoA/FyRoFfdNF0Kx/zwjPefzbyOTzOv4+RoYJnVxhpjtkoiUhCRHhHprPgYsRUpReQwEXl2pM6/GXG8JNlV1VtUdZdqxmRG15hIYCN3Wx3siLnjR8E7UyFeAxCiYWeL9K47M3bRf4F2YP4IXvuPwMN9xFZ7hGGMoPHvwSEfWKHtcWA6bhGEoyyJNcZsxY5V1daKj09WOyBjRtpYSmDvGlAH+9pqBzRWzOq9KLw73CkpqPiUezxUTvRv+l+b9OwA3AIsGKlrF3KpEDirkWIsQV+fItpJ87h55bmvA1YCBdwAs1kjFYMxxtQjEfmFiPyl4utvici/xRkvIleIyHIRWR39e/uKYyeIyPkisjjaf5mItABXAVMrenunDnLdo0XkYRFZLyLPicjpFfs+JCJPisgqEbl8sPbRcTeKyKkVX88Vkf9E/7452nxfFMM7B/YMi8hu0TnWiMhDInJcxb7ficjPRCQfxXiHiNjfkDoTq3YAw+h+kFKA1+MTNvuEs5Lp/LaFXGpptQOrd81S+nqIHwvRoqe6dhtZs+bD/hXXAHcAC5i3dovnfh2KQi71+Me+cua9/wt3miSicUUa54e7HXZnuMsdr/EeWwOsw63A9uRIxmGMMQDZbPau0bhOJpN5paVwnwfuFZG5uI6GDwL7qKqKiAecD5wI+LglwH8KnBC1vQjoBF4VfX69qnaJyFHAxaq6PRt2HnCiqt4iIuOBmQAi8kbgHOAI4CHgu7inbIdszk2p6iEiosDeqvpkdO7D+veLSBz4Z3RPRwAHAf8Qkf1Utb9O9iTgSOAe4ALgm8C7NicOU11jpge2kEv1Ag+WX1oHO6e6UdW/ZDq/syJHAPRqfMUq2lc+qtM/G8+u+j3z1j450slrv2/Ez3+wSfrWoeF6gAC/9dvld0UzItANDPtAMmOMqROXRT2N/R8fAlDVbuA9wPeBi4HTVPXZaN9KVf2rqnar6npcAncogIhsh5v7+6OqulpVS6p602bEUwJ2F5H2qP090faTgd+q6j2q2gd8GXidiCRf8SvwUq8FWoGcqhZV9XrcSpEnVRzzN1Wdr6pl4PfAPsMcgxlhY6kHFtx0Wgc2ENXBKvsBV1Y7qHrWKn2nxwhbFMI+YquAB4HN+UU2LCbJuiXv9G+Y/5vy0YcJ2qNI01M6de9Lym+89d2x69cDT492TMaYrdMw9IwOtxNU9brBdqjqfBFZCGwD/Kl/u4g0Az/A9UKOjza3iYgP7ACsUtXVWxjP24EzgJyI3A+kVfV2YCqux7M/tk4RWQlMw5WDDZepwCJVDSu2PR1dp1/l09luXMJr6siY6YGN3FXC6yaqgxXU5oN9BZLp/PbAMQBF9VcrEgK/fSXLxb4Cd5zqX7lkW1m9OOqFVUWaLgjecnRZvZEeSGaMMXVJRD4BNACLgS9W7Po8sAtwgKq28+JjfAEWARNEZNwgp9zk739VvVNVj8clzZfxYuK8GJhREVsLMBF4bpDTdAHNFV9vu6nrVlgM7BCVSfSbvoHrmDo11hLYB0CKAdILECPcMZnOb1ftoOpVI6WPxQg7AO11va8LgP9UKZwFMQlv+ULsjw/FCEQIewSV1bTPPrt8cicjOJDMGGPqkYjsDJyFKyM4BfiiiOwT7W4DeoA1IjIByPS3U9UluMFaP48Ge8VFpD/BXQZMFJGODVwzISIni0iHqpZwYxSCaPclwPtFZB8RaQDOBu5Q1cIgp7oXeJuINEfTZX1wwP5lwI4buPU7cAnwF6PYDwOOxdXbmjFiTCWwL6+DDWw6rS2UTOcneuhJACW89YpXBi6IZgUYfa7W9qpD/Qe+tYM8f49o0KVIWCLuXRy8+ZBk7yV+VeIyxpjq++eAeWD/LiIxXN3rt1T1PlV9Arc4zEVR8vhDoAlYAfwXuHrAOU/B1bI+CjwPfAZAVR8F/gAsjOptB5tF4BSgICLrgI/iEmhU9d/A14C/Aktws8dsaODUD4AiLlG9AFenWmkecEEUw4mVO1S1CByHq+NdAfwceG8UuxkjRLUaT4NHTjKd/0ic4LMtUtwhQLrXa+NPC7lUttpx1ZtZ6X9+qlX6zhLwOzVRKOMvBN5ayKXK1Y4tmc7PAP7cRHG7BgkmlPDWdWnDJwq51N+qHZtxstlsAng17g3kbGAK0IL7g7gOV4/2KK704+lMJjO2fhEZY4wZUWMxgd1P0F91SO8ugK7Vxhufyh1zTLXjqifJdD7RRHF+gwQ7BUjvem14CuQ7hVzq0mrH1i+Zzn9VCP+vXfpmC0inJu4s4x8Z9cKbKslmszsC78T1fDRv4vB+C3FT3vwtk8l0jVRsxhhjxo6xNgsBwP2K9AZIr482+q4Odmohl1pc7cDqh745JuEOAH0aWwXSiUswasmvFS9VUn91QoIJDVLepaz+icCF1Q5sa5TNZrcDTgPejBsEAvA47tHkI7jBE5243zkTcPNC7oOb7mZH4NPA+7PZ7B+BSzKZTOdoxm+MMaa+jLkeWIBkOv+rZopHJSSY0Kux5b3ETyvkUrWWgNWkZDovjZT+0SjlwxWCtdr4BMjvC7nU96sd20DJdP5THuEH2qVvNq4X9r4y/psKuVR3tWPbWmSzWQ94By55bcKVCFwG/DmTySwcQvsY8HpcjVz/vM0rgO8A11tpgTHGmMGMxR5YcNNpHZogmBDNB7svtdeDWKv28NB9AYrqr8FNnfXn6oa0Qb8L8d5eVH9NQoLxDRIky+r/H67g34ywbDY7AbeqTv9AyeuAH2QymWX9xyTTecEltm24Gtg+YD3QWcilwkwmUwZuBm7OZrNzcInwnsC3om3fyGQyWzoXpTHGmDFqrPbAzhH0vA7p3VldHexNIMdUaf7SujIr/c9cq/R9QsBbpw0LQrwbCrnUp6sd14Yk0/mPeIQfj3phdb023BPgHWm9sCMrm83uCnwPNzhrFXBOJpO5IZnOe8AeuKUbdwd2BcYNcooibunfx3ETm/+nkEuti3p034pLZFtxo5+/mslk/jeyd2SMMaaejKlptCo8qEhPiPQJSIwwCdh8sJuQTOfHxQhOEPDKeN0hXhGomYFbG/CHEG9tCW8tIAnKM3GrwJgRks1mD8atMT4FuB949/k9+z2QTOc/yYvrj38AV986bgOnSeAS3BOArwPXJdP5X57fs98R5/fsdzluINj9uInQz81ms7ZGuTHGmBeMyQS2kEsVgQdenA82bAZqbem/WnR0QoJJ0F8+wCLcIJyaVcil1gF/7NX4SoCEBOOEcG4ynW+scmhjUjabfRPwXVwCevnlvbt97fye/T4MXA7MxSW1W8LD/R89C8if37PfcVf37fwZXDmIB5yezWa/EPXQGmOM2cqN5T8Gd5WJElixBHZTkum8JCi/x0ebFMIi/jrgsqotXLB5fh/grS7jdQl4DQQ7Am+rdlBjTTabPQq3co5fVrn4/J59F67Ulj/iXuvERpqWcAOznsatP76p8o4JwEeWhO2Xnd+z39pejWWjc7wT+E40x6wxxpit2FhOYO/uT2B9wmbQOdGAEjO4V/mEewKU1F8LEgBXVDmmISnkUmuBP/VqbAVAg5QnCDo3mc43VDm0MSMqG8gC3nNB+98u6p2zP8hncAO0BurDDejKAP8HHFjIpY4s5FJvL+RSxxRyqUOAt+DqXH/LhpcBbgc+9YfefT5wa3HGubgFEA4Fvp/NZq2H3ZgaJCLzROTiasfxSojIXBGp1rLpL1H5eorI9Giltc1eeVJEviIivxn+CKtnrM5CAPBgiNcdIiUPjftoMkC2A2w+2EEI+taEBO0AffhrgFsKudTK6ka1WX5fxntXgEzx0cYEwY59xN6KrX39imWz2b2AnCre/8pT77yvPPVoYLAEcglwEXDFpgbRRT9bt0cfP0+m8zNx03Edg5utoNIOjweTP/lcb8edxzU8tEujBK8FfpTNZj+byWRssJ7ZqolIAfdGckdV7Yq2nQq8R1UPq2Jow0pEDgMuVtXtqxxK1ajqM7jBrRs12GulqmePXGTVMWZ7YKM62PtfKCMgsDKCDUim881xgncIxEKkL8Drxc3lWTcKudRqkD/1aWwlQIOUJ4K+L5nO2+PmVyCbzU4HfhgqDTeVZq66r7zda3h58roeyOGWGv7TlswAUcilnirkUt8BjgbOBV62IleXJl7z5969vOeC9hJu6q6fZrPZoa72ZcxYFsMtBjKiRGQsd3oBI3uPW8PrN5rG+ot5d1m9wxMSdMQkbO5z88FeXu2gatCb4xJsA1B05QMrgNuqHNOWuLiI/85Gytt4aCJBsGOR2LHAX6sdWD3KZrOtwPdL6o27sbijPBt2THhxka0XXAN8t5BLrRqOaxZyqS7g18l0/k/AR3G9si9ctIzfel1xdnz32PPxObHn9vZFv5vNZj+TyWSKw3F9YzYlmc7fNZrXK+RSQ+l4+Q7wRRH5uaquGbhTRHYFfoJ747cc+Jqq/inadyOut+430ddzgVNV9aDoawU+CXwGlzPMFJEf4WrfO4AngM+o6i2bCrK/ZxD4AfAlIAC+oqrnR/sbgG8CJwINwN+Bz+I6264CGkSkf5W+nXHlRzuo6goROQOYB0xQ1XUichbQqqqfEZGO6P6PwtXg/xo4W1XD6H4/BMwH3gf8HDfFX2Xc3wFeB6RUde2AffNwUwcGuDfgTwDvV9X7ov0F4BfAycAuItKC60z7Pm4mlqeBT6vqjdHxM4Hf4RZ2+S/wWMW1ksBTQFxVyyIyATed4VtwvfA3RdcZ7LX6MDBbVd8Tnes43Dze04B7gY+p6iMVMf8UeC8wA7gaeJ+q1tRS7WM/gaVyJgLdN5nOi80H+1Ie4TtihG0A0eCtywu5VFDlsDZbIZdalUzn/9qn/rZNUt62QcoTi+rPTabz/yjkUuVqx1dPotH+Z/VqbNZNxZnjF4ftqwYkr324xQb+ORL/n6K65m8l0/l/AmfgfgEDEOKVHi5vw9qwcbvXJZ5+fYuUzs5ms1/KZDJ19zM7FmWz2RZgN2An3PSF2+Ieezbgfog6o49luJlOCsAjmUympxrxjhF3ATcCp+P+v7wgSpiuBc7EJXB7AdeIyEOq+tAQz38CcADQ/z26Ezf93Vpcz++fRSQ5xARnW1ziOw239PRfROQyVV2N+52yI26Z6RJwCXCmqn5ZRI5iwGNxEbkTVxf/V+AQXDJ4IC6BOwSXKINLXjuic0/EvfFeApwX7T8AV262DRDHDRhFRDzcE6HpwBGquqGnS8cDJ+FWFPw0cJmI7KyqpWj/SUAKN5h1CpAHTsElhocDfxWRXVV1eXTPtwNHRHHlgX9s4LoX4f4vvSr6/HpV7drAa0XFv3cG/oD7vt6Ie5PwTxHZXVX7OwNOBI4EeoFbcbPM/HIDcVTFWE9gHwyRrhDKHsR8dLrVwb5UMp2fmSB8rYBEc7+WqO9e6ov6iJ3YSHmyjzbFCGeV8Y/CVmLbXB/u1dihNxdnTl0ati2NVmTrtwT4TCGX2tDgq2FTyKUeTqbz78P1kMwlKnsK8UqLw/aV1/fNmr5f/Lmjt/PXd2az2a9nMpl6mDVjTIne7OyOSxgOBmYzSFf9JoTZbPZxXI/Tf4AH7A3JZjsTuDXqHa10DFDo7+UE7hGRv+Kebgw1gT1HVV94yqKqlYO0vhf1fu4C3DeEc5WAr6tqGbgy6iXcRUTuwP0/36v/WiJyNi6h+/IGznUTcKiI/AOXmJ8TfX0D8BrglmjA0zuBV6vqemC9iHwPl0D2J7CLVfUn0b/LUbIXxyV5MeDYisRuMHer6l+imL8PfB43D3Z/r/SPVXVRtP89wJWqemW071oRuQs4uiLuN6lqH3CziAz6t0tEtsO9IZkYJf/9r8dQvBPIq+q10bm+i0u8X49LaPtjXhzt/yfuTUVNGdMJbCGXKibT+QcCvJkeYXuMoCXA2xdLYCsdnZCgA/pnH+CuQi71bJVj2mKFXGp5Mp2/rE9j2zZKeXKjlCd2qv/+ZDqfr5Mpwaoum83u36uxD99STE5fFrYui97U9HsEl7yO2gC/Qi5Vwg30uhX4BjAVIMDrW6NNS/5bmj59N33+vbv4y1cBPx6tuLZ22Wx2EnAsrvepcmBNGbfC2qPAs7g3POtxvfYAzbgZJrYDdsD1ru+EW7VtV9wblZXZbDYPXJHJZBaO9L2MBar6oIhcAaRx/0/7zQAOEJE1FdtiuN67oVpU+YWIfB44Ffd/UXHfz0lDPNfKKHnt143roZ+M+9m4u6K3UICNjbi/Cfcofg7wAK6n+Txc8vhkVFowBTfN39MV7Z7G9QAPen+R2cDewP6bSF5f0j4qS3iW6PfUIOefAfyfiBxbsS0O3BC1Wd0/GK8i1h0GueYOwKqK5HVzTKXi9YhiXsRLX5OlFf/u5qX3UxPGdAIbubus3pviErZX1MFabxyQTOc9n/D4GGGLgkblA/lqxzUMLuwj9o4GypNihK0+4ewA7024x0ZmI7LZ7ISiet+8tThjxoqwZX0Zv/KR2Xzg9Got01vIpe5LpvPvwU3ndTBAGb+nSxPPPlLeZodOTXzxjHnfWHLWvK/9uRrxbS2igX3vwz0S7f8b8jyu5+Zm4J7NrUnOZrNNuB60A3GPhKfh6u/em81mH8T1wv27Fnplh1iTWi0Z3NLM36vYtgi4SVXfvIE2XbjEsd+2gxzzQpmQiByMq189HHgoSn5Ws/m97gOtwJUovEpVn9tYDBVuw/X8vhV3jw+LyHTcz2Z/b+QKXK/vDODhaNt0oPIag537EeBnwFUi8kZVfWyQY/q9kGBGZQfb89KOssrzLwIuUtUPDTyJiMwAxotIS0USO30D8S0CJojIuEHqnjdV1rUY2LPiuhLdw2Cve80as7MQVLirjN8FL8wHu2+1A6oh+8QJdgIo461XpAf4d5VjesUKudRiRS4vudXEohkJODWZzm8NP+9bLJvNeoFK9o7S9L1WaXPYi5tXN3IH8NlqJa/9opXXPo8bFKEAJfyubo0vWRSMG39bacZPT8t8Z0N/qM0rkM1mJ2ez2TNx9YbH43rGbgQ+BRyTyWS+nclk/rslA+oymUxPJpO5I5PJfB9Xl/d+4G+4ur49cAto/D2bzb4zm83a/M4boKpP4pb//lTF5iuAnUXkFBGJRx+vEZHdov33Am8TkWYRmQ18cBOXacP1si8HYiJyJq4H9pXGHuIGV/1ARLYBEJFpIvKW6JBlwMRoQFZ/m27gbuATvJiw3gZ8pP9rVQ2APwHfFJG2KEn8HG4w2aZi+gPwFeA6EZm1kUP3FZG3RbMMfAb3tGFDq1heDBwrIm8REV9EGkXkMBHZXlWfxtUzZ0UkISIH4Z5yDBbbElyt789FZHz0fT0k2v2y12qAPwEpETlcROK436l91Nng7a3hD/qDAdKpEHgQ89DpyXS+5rrCqyQVj8oH3OwD3FjtBGUY/a4/AUsQdAjhzrieHbMBoXLy3aVpb18etjR1a/y5ig6V+cDnCrlU30aaj5pCLhUWcqnzcDVbXQBFYmv7NLZiVdjceldp+z/83xm/PKyqQY4h2Wy2MZvNnopLKI8DQtygkrdnMpnTM5nMbcNZe5zJZDSTyTyQyWTOxg0iOQfX2zQV+AIukT0hm81u9mTuW4mvUzGXclT3eQTwLlzP21LcYKn+NwI/AIq4pOcC4PebOP+/cInT47jH0L0M/gh+S3wJNwPAf0VkHW5BlF2i+3gUV5O6UETWiEj/3/GbcI/g51d83YZ7GtDvNNzvioW4GutLcIuobJKqXoB7Ta+PZgEYzD9wdaWrcbW1b6sYwDXwfItwbwC/gnsTsAj3c92fj70bN3hrFa5H/cKNhHcKrnf5UdxTkM9E19jQa9Ufw2O4AWc/wfVQH8um63xrjqiO/QH5yfQV57ZL79viBO0ewboTvFsu+Gr8kl8CC5i3duy/AINIpvMJn+DmNinuqRCs1cYnQE4r5FJ19Q5sY5Lp/DdbpO+DccK2PvVX9JC4BTjFZqF4uWw2u9P9pW3/tSCYOKVLE4tK+P3TrzwCfKRW39gk0/kdgR8CU0FpkdLUOEGHT9jbKOV33Xr2u6+tcoh1LZvN7gd8jRdr424EfpzJZJ4Z5Tg84DBc3WX/jBTP4KY8+ncmk7H/06Yqomm0Xpieyoyesd8DO69D3uTd09dEb0xQUSTxjG6zD+4xyVHM69hal5c9JE64LYBLVmQl7jHxWPLb/oUNEhKMB90dN5efqZDNZmNPlif8ckEwcUpR/dUVyeti4NO1mrwCFHKphbh6zPtA6NL4kjJed4DX2KmJP+6e/vvbqh1jPcpmsy3ZbPYruGlzpuF6xT4S9biOavIKkMlkwkwmcz2u1+gruMFh03ELaPw2m83uPtoxGWOqa+wnsDDrHf7NbYF63Yqo4sUf1x0m4+YePBjYWF3LWHZ0PFo6tqT+OuBf9Tj368YUcqkFZfx8gHQL+A2Ux+FqYbfWNy2DeiYY96WHy1P2D5FSN/Hno81rgE8O1wIFI8mtwsbHgCtBtEsTi0KkT6DRE/3ljul/fty+50MXLR18KW6i+jIuiT0lk8ncXdXAeCGRvQY3BdTZuMesezL4wCNjzBi2NcxCcMDB3gMLfILeMr4C/nptnnBPOLt9jvfkOmB/Bqy6MdYl0/lxPuEbfLRBISzhdQFXbrJhffptr8aOa5FSc4MEE/o0thfIvrhC+a3eqWf+cM5D5SmnB3het8YXRfO9lnE1r6Pe07aloinzMsDTinysUxOL2qQvGSNsaaT8lW7i05LpfDZaYtoMInpMPxe3ApqHKx+Zl8lktni+32Q6346rXZ2Em0B+IjAh+mge8NEYXVcGfIS4ASa90ec+2K8X6PIJ7tjOWz/t2bBj5vnp/M6FXOrxLY3VmC2hqvOqHcPWamtIYCe1SO/6KbL6uefYZjJIAyKJ64NXT5/jPfkkbu65rc2b4wTjAcr460GewhWBjzmFXOrRZPqKf4WU3xstL9teJPZBLIFl7td+HF8YTPpjr8YTRfVXV0yZlSvkUvdXNbgtENU2n5dM5xeFePO6NPFsixRnJCQYH6qc1Et822Q6f3rUY2sqZLPZcbgezf2jTRcCv8hkMoMORKkUze6xPa42dTbu0f720ccrHp2+MQE+z4bjwE3B9TxuYJExZiuwNSSwK4DpO3vPPr04nLy7Ig0giQd15gxcjd/Tm2g/Fr05LoFbOtaVD1w5tgc2yXl9Gks1SWm7aHnZ1yTT+b3qMUkbTs+F7b9Zp43TBpQO/KWQS11WzbheqUIudU0ynV9axv9+j8ZjzVLavlHKUwKVg0rEfpdM5z9dyKUK1Y6zVmSz2Zm4gXDTcKOoz8xkMrcPdmxUirEdblWevXAjxGfj1mGvtnXVDsAYM3pGPIHd84I9BVdnegDuMdIK3GChBQ+874ENJk3D1W63qdt66ZWrZ+xXfvSZG3WfIgKKJJ7WKTNwy+jNr4U4R6td0LP9m33/vSk/9FsVKUXlA/+qtTiHs10h98D9M9NX/LuR0rt8tDFG2FzGPxX4VC3FOZrttnn88zutDFveDtCt8cVR6cC9RBOg10qcW9qubTceWP9Ibm6R2A891USjlLdpltK0TpVSgH9+Mn35F9p2++qaasdZ7XbZbPa1uIFQrcAjZSl//rIZl7X/5YK/nAxMUpUVxRVvXFRccfi24M3BrUw0yFMrBSk3iNfXgoQx1Ctr2NCFxvo2Pr/98LXzWx/v2POCtGzsdTHGjB0jOo1W9Ev0KNxgqXW45cj6lxG8BbhqsF82w9pOtXn3YnGfI9aXvPOWzzugKI1TQCWuxdXfiv/qc4f4D1yy58zpVD3OUWrX9/yRM701+765UaWtJGFft1ec3zr7u2+qtTiHu936R3L7NlL6S6OUJ5fxOju1YREEp7Tt9tWZtRTnaLTTUuvEhqc++d4gbGgpqr+6m8RSXM/bSYVcakWtxDkc7dY/kmsD/VazlI5LEIxTKK/XhqdCv7exYeINDyQm3nJPLcRZjXbZbPZE4HRc3en13X73mVfucOUbw3Lr4eV1e7YH3bO2C/smz9IwMU7Dhk7CprWDJ5UKXk+HeH2t4AXuzZB6EPpoYrUGzQ+DLANWRh+r3OewMzH5X/v4jc/tgVdaLV5pPVJuFCm3atBye/czp15L2EAUX0P00QhBY2LSDW+Q2Pr9tNwaaNAMGm+LT7il4Dcs/9eGXhdjzNgy0j2ws3C/RAu8uLRZD+4X2MG4eqXBBlANXzuRnocTietXjPNf3bR6zXPFYMp4RRLraOmaW/rSmoXfOFa5YM/ZVY9zpNupHjyrVOpa0rntnKKGrYInAdobb7+vKzpvbcQ5cu3uLuHf0kD5hGh52YYw1vk5XM9ULcU54u0anz357WWNjQvRvp4XSweyhVxqxcba1cv9VbYr5FJPJtP5T/VobJkn+vEYYUuL9CW7pNhbXHnIa4LeqaXGqX++SSSsy/vbknaJIPFkNps9ATgx2vfbP/Ts/adi0+IPyjMfeH/Yt+1EVCoz1T7x+lpV471o/OWLWUi5wYt1xvF6H/fia5Z5iVUrvMSKVV7D4jVe49KJIuF5D7zvgZfFuaf7vXsUbiWlyoRTYNU+bbtk7t5Iu0m4OWkHtNvo62KMGUNGehqtA3A9AAPfDWu0ff+XtRiJdiL6fCz29NPNXQ91auPKAL+sePEQb9+NthvtOEeonageMKe3b7tXrW99Y2954hTB80FppDexT+Nt3aJaE3GOZLtCLqUB3i/6l5dtlPJE1D+83LVjrJbiHPF2y47ct1Sc/CqAXgk71ZUOXFrIpf5TU3EOY7tCLlVSvGxZvTNDpM8nbGoO/VaAoGv267uf/si7wr5JzdWOczTaNZQbeg9adtBPgBM7wwQ3FHe84fye/fbrJX6VFid+Puybsu2A5DXiBeL19a/u1Afcg1vJ6LPNM879efOOPzi3ZebPf9+0/SXXNWxz9b3xcXc94zctXicS1tLrYjZCRK4SkfcN97GvlIhotMStMS8x0j2wk3CPrwbTzYZnABiRdrGWx9aU1+3RDeBL2IyyXy3GOdztppfKu84qlabd07tfAxrzAULCUnN8xfI9WDqxu9S422DtRjvOUWh3ewn/jgTBUXGCdiEMiysP3TvWsvCJGotzRNoF3TPG+WvnvEMQr4z2lSQsAQuAH9VSnCPRLhqk+MvXfOXS1SX0dzEk3qR09Iiu1eKEmd2L3v/BhsnX/i3ece+qasY5ku0m9k4ct8eK/d/2fHHK1HtLU4rPhe1ryvhveOEACWNRLfRLSRh48VXPeI2Lny6tPjAHPFbIpcr9u/e8ID1nOOMcwXZjjoh0VnzZjHtz0T+f90dUdVPLwr5AVY8aiWNHS7TM61NAXFXLmzjcjAEjncCuwE2p0jPIvmY2PAPAiLSLtT56fy/eQYD6aKOg2yfT+e3adqutOIe73ZzevgnrPC9Y2rfLdh5+HCCUoLRtw2OL13leMKe3b3wtxDnS7Qq5lCbT+Z+W8A6ME7Y3qN/Y2zdlt3LXzAmxlqcGTthfd/e3sXYaxj2WnPAeX/1WRbXHCzpRrxf4yiBzo9bd/Q213Z1nv/PSQ75z2mt7Vr/2oxBvDpVyn2gXYaKt7/mjTwn7tp2fmHzNP6sd53C206DBb1/+xtf762cffWvY3lrGK3WFTYtDvJdOkaVeGQkSIKH4Pau8hqVP+s0LF8Y77n1G/N4O4OknvnT2Q7V2f5vRbvS5lR4HHUw3HMuYq2pr/79FpACcqqrXDTxORGKW1JmxZqRLCO7ADRwY+EhKou3zR7OdxLpvA7k/QHoAYoTNwJxai3O42x3Z3b1qabBtS1d54nhBfECVsLxD0/+Wrfc8/8ju7tW1EOcotbu5rN69AAmVRoF4cdWhr6/BOIe1XXHJ2w6JldtmAfRBZ0iIJFb/pJBLDTZJfd3d3+a0W73NjT+bNPnKq8dJV7ERaY8jjQCoeKW1ex/a9cSXj0qm84Ot7FQX9wfcoeq1l9bsO7170fuOLi/43Fe71u574spwXGtJKHdq/OmXJa+AIvfH2u+9r3Hqpb9qmfX9XzZtf8l1iQn/XSh+b1Br97eF7UaXS16Pwi1bPj3aOp1RWMZcRA4TkWdF5EsishQ4X0TGi8gVIrJcRFZH/96+os2NInJq9O+5IvIfEfludOxTInLUFh47U0RuFpH1InKdiPxMRC7eSOxfEJElIrJYRD4wYF9KRP4nIutEZJGIzKvYfXP0eY2IdIrI60RklohcLyIrRWSFiPxeRMa9gpfW1JCRTmAX4Ea9JnErsDRFn5PR9g2t8DKS7e4pq9cNECNoBvat0TiHrd0BPb2Pemv2FvAaAAKCcktiybrOxnWt+/f0PntAT+8jtRDnaLQr5FJhH/EflPG6BZFEmCDs22a/oHdqspbiHM52pfW7H+B3zTrKg1iABn1euSR+z+2xlsd/Wktxjma7Zyfc/+vtJl5384zYsp4mZXwMbULKDRo2dGrQuitwaTKdP27AErQ1f3/JdH7m+kfOeUvXk196Y9/yN38w0bP9oY3qTxaQogR9XeovVo1X9lw+CHwfOLZt52+8tXHKVT+LtT7ZVqv39wrbjbbKwXQrcT3GKxm9Zcy3xa14NgP4MO7v/fnR1/092Bv6HQCu1/gxXM/xt4HzRAarj97ksZfg3lRMBOYBp2zogiJyJG5mjDcDOwFvGnBIF/BeYByQAj4mIidE+w6JPo9T1VZVvR33puYc3GpwuwE7RDGYMWBEp9GCl8xHuD+uNmk57od5qPMYDmu7ZDr/mjjBhS1SnB4gPeu18dZCLnV8rcU5rO3mdcw+vu/rly9iShIhXpJiz6tar5//ce+qGw/q6W3x4DzmrR101G5d3N9mtkum814TxRsaJNgvhNI6Ys/6zQsfbJ5+/u21FOdwtEt+5S/tcbimWcN9RFQ6heVljS0Ejiuc/fY1tRJnNdp56s06cNmB53T3TD/kgeKM1jXa+Gyg8fUDOvbuAb5TyKWeqNX7S6bzE4AjcH/Qo3p2lRbpnR4nbEeUHljTpw3PR/OrLgKuAq4euFxwLd7fcLYbVfM6TsYliisH2TsReJp5ay8ZrstVlhCIyGHANUC7qvZu4Ph9gBtUdXz09Y3Axar6GxGZC5yhqrOjfc245HE7VV061GOBBLAwiqM72n8xgKq+Z5CYfgs8r6rp6OudcYnxTqr6sr9RIvJDdyr97FBqYKNkN6Oqrx70RTR1ZcQT2FqTTOcbBb2pQ3r3AHSNNj4OcnQhl1pa7dhGyk7py3Zspu+6uOj2gPpaWvbXhnnnby8rEkTzQg5HPVY9mZm+4rg26fudhzZ0a3xxkdgK4PhCLvX8JhvXCdd7qLlWKX4gRthcVH9NN4klwMcLuVRtPGatsmw26wPndIbxI+4s7zDxmWDc6hBvYE1wCPwF+HWtLEObTOcbgEOBo4HXU/E0zSOMtUhxBx9tVAi7NfFsCf9ZXEJzJfDw2F55r0bM6/h09K/BanXdymXz1g4cQLnFBklgf6+q0yr2NwM/AI4E+sc9tAExVQ0GSUpPVdWDKtorUSI51GNxPbKXq+o2FfvOAXbYQAJ7NfBPVf1Z9HUD0Ftx3QNwC2/sgUuOG4A/q+opgyWwIrIN8GNcj3cb7v/JalXdYbNeXFOTtoalZF+ikEv1JtP5+wNklo82xQgby/hzcL/Yx6QS8SP6QDxKZSHsmynPF7aXFY8R9VhsbckrgCJXBsgTHrpHtLzsWpAPAd+sdmzD6LgEwdtihM0K5R7iy4ALLXl9USaTCbLZ7BmtXqn5sPjC1z7qTfbml3YIQ7zK8ioPN2fqccl0/i/ARYVcarBetRGVTOebcMnq4bg/yC9bvtUnaGyV4g7ifrf3ltT/Qwn/EmB+5cwBZlRUe7DZwN/rn8ct/XtA1Iu6D/A/Nr7k2Su1BJggIs39PbC4x/gbO75y//QB+y/BlT0cpaq9UQ/spGjfYH/Hzom276WqK6Me2I2VTZg6stUlsJG7y+q9xZegKU7YUsbfjzGawEY1fEfEJWhXRDu1cdmd7Ppd5q29vNqxVVMhlyrPTl/+vZgUf+2jDXHClhL+8cl0/uJCLlU7o5i3UDKdnyFouklKUwB6NP68Ig8Dv6hyaDUnk8kUs9nsF0T42W6x5Xtt561feUXfrs+WiA18zNgIvAc4MZnOXwn8DXhkJHszk+n8ROC1uN7WA3E9ToNKUG5vltJ2E7zunm28ztsF5v7hGx8fs0+W6sAduJ7CVbx8wYVqDDZrwyXTa0RkApAZ6Quq6tMichcwT0TOwI05ORb45waa/Ak34OxCXK3wwBjbgFVR8ro/8G7ckwVwZSQhsCNuMYv+49fi7nka8IVhuTFTE7bWBPaeMl53A8HEaD7Yfasd0AjaySOc1f84sYS/FreCzVavjP83Rb4o6G6NUppcUq8L5BPAF6sd2yuRTOfjwDebpDRdwC/jdRXxl+GmzHrZ6HMDmUymJ5vNfho4d5zXu/PJjfcWryru8s1lYdtcYNqAwxPACdHHgmQ6/2/c/6knXmkym0zn23FJz364xHXnTbdSxkuPt3NsRXyGv3pBi5T+BpyTyWTse11d/YPNDmbwJX1He7DZD3E9mCuAxcD3cD/DI+1k4He4WuD5wKWAP9iBqnpV1Kt6PS4ZPSNq3+/jwPdE5KfATbiEd1zUtltEvgncKiJxXKlEFrgQl8Q+CVwEfHZY785UzVZXAwsv1MHe0iG9uyvoWm18LKqDXVbt2IZbMp0/rZHS5xqlvE0Jb22XNlxayKXsP3Bkt/RlxySkfImA36WJZ0r4XcD7CrnUYPNd1oVkOv+pGMFHW6U4Q0HXa8PCEO+MQi61Vfe6D0U2m23HPWLcHVi2Omz81GV9exwAvA838GZj1gD3Ao/gavEW4f5orynkUiG88ESkCfdHdxywPW70fBLYlZc/Mt2Y5XGCm96UeGK3KV7nq0QIcUnJnzKZzNb3i70WvTgP7MsGm22NpVsAInIp8KiqjngPsBnbtsoEFiCZzv+mTXrf5qMNnZoolPG/UMilxlQZQfTH8h9t0nugjzZ2afzZErHPjrX7fCWS6bw3XrpvUWQfNytFQwHkLuBj9TjQJZnO7w/6i3bp29FDE70aW95L/I/Al+vxfqohm8224lYn2xuXgJ52fs9+TwPHA3OBbTbceoOUFx8jv5LpC5cB/wauO7nxnp6EhDnctEjrgHQmk7H6ZlNTROQ1uDKKp3CzZVwGvE5V/1fNuEz9G+l5YGvZ3YF6XfDCggZjsYxgd49wRkX5wCrcYxcTKeRSYQk/rRBEg/qacY9vX1ft2DZXMp0fD3y9kfJED02ESLGX2MPA2Za8Dl0mk+kEPgnciet1/c37m+7at5BL/QlXv/c54D+4R5xDJbjft5v7O1eBh4Df4HqBj3l/010/eH/TXTMTEl6AS14XAO+15NXUqG1xJTaduBkBPmbJqxkOW3MP7P4Jyhc3S2laGa+rUxtuL+RSx1c7ruGUTOc/10jptKh8YF2XNlxUyKXqur5zpOz35Uv/XcZ/bYB0r9eGp0GeAk6ql5HbyXTeA37gEb6hTfp2FJBOTTxVxj+lkEvZH4stkM1mE7hBJG+Blz+ej94wHAIchnsD3DwMlw1xtXoPAncBdxRyqbUVMbXiarSPjjZdDnw7k8kMOtenMcaMVVvrIC6A+8t4a4FpPmET6LRkOj+1kEstrnZgwyFKaN4Ul6ANoKj+OuDa6kZVu8p4n1e42UebY4TNZfyZwP8Bf6h2bEN0EuiBzVLaVkCK+GvK+D+15HXLRbMTnIGrZT0VN4J572w2e1Ymk+mO5oT9B/CP6P/bTsCewMzoYwpuvs32AacuAatxNbPLcaOtn8Y9Yn2skEt1M4hsNvs64Gu4EoZe3ECt/LDdsDHG1JGttgcWIJnOn9suvSd6aGK9Jp4K8L9WyKX+Xu24hkMynd/HI7ygXfpmK4RrtfE+kDcXcqnB5iQ0wIFfueTvXZo4oqIWthN4a61MXr8hyXR+d+C3CcoTm6U0VSHo1IbLA7y59dKDXOuy2ewRuBHR/fN3npnJZIY00C9KbsGVDwhQ3pySjmhg2ad4ccT4Q0Amk8kUhnoOY4wZa7bmHliAO8rqHZOQIBEnbA7w9wfGRAILHJEgaAco43WC3GzJ68bFCE7z0AeApgRBW9H99/g4Nby4QTKdbwXOETTRJKVtAIoaKwR4X7DkdfhkMplrstns47h13ncEzs9ms78Hzt3U4/v+GQjYvJpZstmsh0taP46bsaCEm8f395lMJtisGzDGmDFma++BfVWC8mXNUppaxuvs1IYHgTdX/MGpS1GPz9Vt0jvHR5ui2Qc+Usilbqx2bLXujV+98EerwuZTQ6S4ThsWgoTABwu51P3Vjm2gaJaJbwJHtEhxapygo4zX3aWJE5/KHXNDteMbi7LZbAPwEdyCBh7wPC6pzGcymWH5vRElrm/ClS3sGG2+B8hlMpmFw3ENY4ypd1vzLAQAj5TxngfwCZtBO3B1bPVuX49wio82RbMPLANuq3ZQ9UDQLzZIeY2HJhooj8M98j0jmc4nqhzaYN4OHBEnaI0TdCiowq8seR05mUymL5PJ/Bh4P261n21wA73+mM1m35bNZl+2vOtQZbPZ9mw2+07gz8DZuOR1CfAl4COWvBpjzIu26h5YgGQ6/5126f2g9+J8sN8q5FIXVjuuVyKZzn+1kdKpFbMP/KqQS9mk0UN03Bm//vAzwfgfKATrtPFJdb2w5xZyqV9XO7Z+yXR+b+BcQRNt0jvLg5jCvWu16Q2FXKpY7fi2BlFP6ZHAx4Dtos3rcVMG3QLMj6bk2lB7wU1u/zrcMrEH4Vb5ArdS0vnAFbailtlSInIjcLGq/mYYz/lL4DlV/cYwnW8eMFtV3zMc5xsNItIJ7KWqm3xTuTnHbmYM8xjl101EpgMPAx2qWvUypq29BhZgflm9dyUkaIgRtpRdHWzdJrDJdD4GHD5g9oFrNt7KVNo3vvjXPZr48PKwZbdGShN7SCwHPpBM5/9dyKWq3guWTOcn42oxY01SmhIlr+u7NXGyJa+jJyoZuDKbzV4LHA6cCOyFmyv2WIBsNrsYN0/rGqAL99SrHZgEzCZaBrPCf3F1+DdlMhmrYTabJCIF3IwXAe5n7ErgNFXd4JunV0JVPzoS5x0NInIYLqHf/pWcR1VbR+LYWhP9bJ2qqtcBqOozQM3cjyWwcEcJrytBMCEuQWuvxuck0/lEHScC+3uEE/vLB8r4S3BLF5ohymQy+tEzv/+Jtdp4jcLEPg3XhK7a5qxkOj+3mj8bUSnDt4CJcYKWBME4BW2W0mfvO+cdhWrFtTWLekivBq7OZrM74uaGPQTYDZgafWzIeuA+3MII/8lkMktHOFwziva8YM/+pWQPwL1pWQHcASx44H0PDOfjz2NV9ToRmQb8CzdjRnoYz7/VEJGYqtqbxzqwtdfAAiwq4xcAfLRJ0EbcEpL16ogErve1jNepyHWFXMoeQW6mX379c3fM9Ff9U0CapbRttArozrgVmqoiGrSVBvYS1G+W4lSA8V7PX28/+6R6ma92TMtkMgszmczvMpnMB4CDcb2yXwS+Dnwf+A5wJm5arGOAN2Yymc9kMpm/WPI6tkTJ61HAB4Hp0ebp0ddHRfuHlao+B1wF7FGxeYaI3Coi60XkGhGZBCAieRE5rbK9iNwvIieI8wMReV5E1kbb94iO+Z2InFXR5ngRuVdE1onIAhE5Mto+V0QWRtd9SkROHso9iMhxIvKQiKwRkRtFZLeKfV8Skeeicz4mIodH2/cXkbuiGJaJyPcHOW9L9NpMFZHO6GOqiMwTkb+IyMUisg6YG53v9iiGJSLyUxFJVJxLRWR2xevxs+j1XC8id4jIrC089ojovtaKyM9F5CYROXUYXrcdRORvIrJcRFaKyE+j7bNE5Ppo2woR+b2IjIv2XYT7ef1n9Fp9UUSS0f3EomOmisjlIrJKRJ4UkQ9VXHOeiPxJRC6M7vUhEdlvU9/LzbHV98AWcilNpvO3Bci+bhL7oLlEbH/cMpJ1Jeqde0Nc3PRZVj7wysz2V3xqTdh48LKwbVKcoK1EbD3w7mQ6f3shl7q9CiF9EDgOlBYpThWItUvvwnHS+4EqxGI2ISoBWBh9mK3PLNybmALRO2CgB1gVbX8ct+rasBGRHXCrtP2tYvO7cYn0IlwCdzrujfAFwOeBn0Rt9wam4UoQjsA9RdgZWAvsiiuDGXi9/pK7dwD/xtWCt0XJ4o+B16jqYyKyHTBhCPHvjFs85gRcLflncQnU7rjFQT4ZnXOxiCQBP2r6I+BHqnqRiLTy0gQeAFXtEpGjGFBCICIAx+MWrnkv0ADsHl37LmD76HX7OPDDDYR+Eq4e/h7c6/pN4F2bc6y4NxZ/AebiVtj7BPAh4KINnOcFm3jdAuAK4HrglOjr/kRSgHOAm3GlTX8F5gGfUdVTRORgKkoIote80h9w81JPxf2MXCsiC1X139H+44C34Qa9ngX8FHitiOzChr+XQ2Y9sM78kvpdAHHCFtzjnnr0Oo9wXMXsA88Ad1c7qHr1zXlfW7VHbNkZjVIqNUl5Cmj//5ezkun8xh4LD7tkOp8CPgrQQHl8jLC1UUrd0/y1x1921oeqXkxvjHmZA4B1vJi89tNo+/7DeK3LRGQNrhTlJtwsFv3OV9XHVbUH+BOwT7T9H8BOItI/884pwKWqWsTNOdyGS0pEVR9R1SWDXPeDwG9V9VpVDVX1OVV9NNoXAnuISJOqLlHVoSz88U4gH52vBHwXaAJej0u8GoDdRSSuqgVVXRC1KwGzRWSSqnaq6n+HcK1Kt6vqZdE99Kjq3ar6X1Utq2oBOBc4dCPt/6aq86PSg9/z4mu8OcceDTykqn+L9v0YGOpTmY29bvvjEswvqGqXqvaq6n8AVPXJqE2fqi7HPSXa2H2+IHqzdBDwpeic9wK/wf0c9fuPql4ZDfi6iBefbm/sezlklsA688t4XQAxCVuB3ZLp/MDlH+vBwMULri3kUpbcvALtXt/v94otvcUnjDfjFgoAOoDvJ9P55tGIIZnOH4Z77IxP2NAo5SlxgmAXf8Wn/vCNT1jvnjG1aRIw6LLA0fbJw3itE1R1nKrOUNWPR8lqv8okqJtoEI6q9uES2veIiIfrGbwo2nc9rrfsZ8AyEfmViAz2N3EH3CDFl1DVLlxS9VFgSfTIfNch3MdU3Ep3/ecJcT3H01T1SeAzuB7C50XkjyLS35HwQVxv8aMicqeIHDOEa1VaVPmFiOwsIleIyNKorOBs3PdzQwZ9jTfz2KmVcaibIurZIcTe33bQ1w33PXp6sLpeEdkmeh2fi+7zYjZ+nwOvuUpV11dsezq6Zr+B99oorsZ4Y9/LIbMEFijkUqvKeA8ohB6a8AjjwGurHdfmSKbzjcAhFeUDa4FrqxtV/ctkMuE0f93nZ/srlyYkGB8naIl2zQa+XrFM6IhIpvMHAznAF9RrkeL2Psoe8aUXXvCN06zu1ZjatQK39PBgmoHloxjLhlwAnIybRaNbVV8ojVLVH6vqvsCrcMnhFwZpvwhXKvEyqvovVX0zrqzgUWAo0xAuBmb0fyHu+f4OwHPROS9R1YOiYxQ3oBVVfUJVT8LNy/wt4C9RGcPLwtrAdQdu/0UU806q2g58Bfe4fSQtwZUrAC/c+1BnS9jY67YImN5ftzrAObh73yu6z/fw0vvc2EDDxcAEEWmr2DY9uuYmbeh7uTksgX2B3Bb098K6MoIDqxzQ5jrII2z30caofOAp3Ohm8wplMpnHd489f/YUb/26JiltJy+WEhwGfG2kkthkOn8o0XRZoDRLcaqHJvaILb0z6a8Z7I+JMaZ23IGrKxyY+Ei0veqzw0QJawh8j4paSxF5jYgcICJx3NRcvbjHvgOdB7xfRA4XEU9EponIriIyJRpU1AL0AZ0baD/Qn4BUdL44rka3D7hNRHYRkTeKSEMUT0//OUXkPSIyOep5XBOda7DrLQMmikjHJuJow5V5dEY9xx8bQuyvVB7YU9wguhiuBnbbIbbd4OuG+zlbAuREpEVEGkWkP79pw31v1oibwWLg35VlvLga4Euo6qLo/OdE59wL1xP++00Fu7Hv5eawBPZFt5bUJbBxCVqB141079owqygf8NdH5QN1vSRuLfFEf7df/NlrO6Q3aJbidhVvTI8FvjzcPyvJdP4duBHrcYBGypPihG17xpYumBVbdUomk+nZ+BmMMVW2ALegRRKYiKtJnBh9fQuDPHqvkguBPXGPj/u143pMV+MeC6/E1VW+hKrOxw3Q+QFusNdNuB41D5dELcYNWjsUNwhqo1T1MVwv4E9wPdjH4qYIK+JqJnPR9qW43tavRE2PBB4St2jAj4B3qWrvIOd/FDfwaGE0Wn9Dj61Pxw1+Wx+9DpduKvZXSlVX4AaSfRv3eu+OG0TWN4S2G3zdovrTY3FPDZ/BlSW8M2qaBebgvnd5Xjr4D1wP7RnRa3X6IJc+CffzvBg3f3VGVYfy5Hdj38sh2+pX4uqXTOdjPuGtbdK3h0J5rTY+AXJKIZd6pNqxbUpUi3ldm/Tu4qONXZpYVMJ/RyGXerDasY0l2Wx2emeY+NPNpZm7rgkbV/URX1WxOw+c9UqnLIsWovgEFYXwCcrtzVKatmds6eLZsZXvy2QytiywMXWgYh7Y/XE1r8txPWLDPQ/sFhOR9wIfjh7nmhoR1SU/C5ysqrY8+CC2+mm0+hVyqXIyfcXNIbKLh8Z9wsYA//VAzSewwKEeYeuL5QPeE7ipLcwwymQyz2Sz2TMOihe+f0spOX1V6PWW8fsHaaSA7ZLp/FcLudQW1bZFMxt8E9cbAkCMoLlZStvtFVuyZFZs1TcseTWmfkRJ6pMM83RZw0VEmnE9oz+vdiwGROQtuNKTHtzjfMGtzmcGUU+PyEeB3FZWrxMgTthK/dTBHtlfPlBy5QPXFHKpmnh3P9ZkMpnr2r2+3xwULzwzTnqmRAP++s0B/phM54+IFh0YkmQ67yfT+ZNwj7ZeSF59woZ26Zu2f3zRc7Niq85lCPMBGmPMUETJ0nJcneMlVQ7HOK/DlZb0lwGcMGBGCVPBSggqJNP5beIEN7dIcYcA6VmvjQuBNxVyqXXVjm1Dkun8BODqNumd7aMNXZp4poR/fCGXerzasY1V2WzWB368Lmw4+D+l5KTnw9ZligwsQL8P+B1w64ZqkZPpfAvwFtzk2S8ZbeoTNE70erY7IP7Mkkledx74ciaTsZpmY4wxBktgX2Zm+oo/t0vvUQKyVhsfV+RLhVyqZlezSqbz7/IJv9ImfbMUgrXaeDXIO60HdmRls9kW4Nxe9V91azHZtigct36QJBbcAIb/Ak/gRsd6wBTcSjH74orZXyJG0JT0V3e8Jv7s8kYp3wCkM5lMcaTuxRhjjKk3VkIwgCK39E+nFSdoxS2nV8uOHlA+kLfkdeRlMpku4FONEix4Y2LBmjmx50KPcLCygQm4FVY+DWSArwEfxq2Q8rLktZFSYv/4Iv+geGFpo5T/BXzRkldjjDHmpSyBfbn/lPrrYN10WgdGI8NrTjKdT4LuHpegA6DkFi+4urpRbT0ymcwq4EMiPLZXfKme0PBQb7v0buHUOBrM8FatOKHxoWCX2IpOEf4OfDWTybxs9RRjjDFma2cJ7MvdV8ZfDBAjbAVtww3OqUVHxwibPDQRQrmEd3Mhl1pW7aC2JplMZjXwEeDmDq+v4e2ND846IvH4LTGCa9nwMpIVdMkUb/0N72h4YMUbGxZOapJyETcP4NmZTMaWATbGGGMGYTWwg0im82e2S+9nPTTRqYmny/i/K+RS3652XJWiifMva6Y4JyHB+D71V/aQ+GQhl7q82rFtjbLZrAfMxZUHxICuknp/ubk4s/BMOL4dt8ReI25alBUNlJYdEF/UsKO/6hAR9olOsxDIZDKZepi6zRhjjKkaS2AHkUznD22ieFGDBBOjxPBBIFVLtaXJdP7VoL/pkN6dBPxOTTxWxj+kkEt1Vju2rVk2m90Rt4rL/hWbn8PNA7ket7LWVGA3XpyHeT1uScY/Wb2rMcYYs2k1WdtZA+4o469sIJgYl7C9R3UbkF2prUUNjooTtAj4AdJXxvuXJa/Vl8lkFgIfz2azewFvxy2hOC36qBQCDwJXAFdmMpkhlBsYY4wxBiyBHVQhl+pNpq/4t8KOblUubQiQQ6mRBDaZzjcARyReMnhLrqxyWKZCJpO5H7g/m83GcGuD74grIQiBJcCTmUymZucXNsYYY2qZJbAbJDeW1H9XQoLxCYL2Hrw3AL+sdlSRwwVtjxG2AZTwFwG3VzkmM4hoFoEF0YcxxhhjhoHNQrBh/ynhrwWISdAGzHLTVtWE4+MEbQJSxusO8P5eyKVsuiVjjDHGbBUsgd2AQi61pox3i0Loow0eYQK37GdVJdP57YF9ExKMAyiqvwb4RzVjMsYYY4wZTZbAboQiV5fx1wMkCNqAtyTT+cFWWxpNx3mEiRhhs0JYxru9kEstrHJMxhhjjDGjxhLYjbu+pN4agLgrI5gO7FKtYJLpvA8c20B5HEAJf12I99dqxWOMMcYYUw2WwG5EIZdaV8a7NiojaPII41SrjGBeh7zJu/vECazbpUX6JvsEMU+D1RNZe21V4jHGGGOMqRJLYDchxLuyooygA1dGMLqv27wOAY4qEvt8TMI2EE/Q4HDv7lV3N37ssGi/McYYY8xWwRLYTbu5pN5yADfvqm4D7D3KMcy6L9wx9XA4Y1KI3+CWA9Ouo/351wEHA7NGOR5jjDHGmKqxBHYTCrlUTwn/StAwTrl5MmunHeQ98FXmdcwexZ7PA84vHzkTxFekAWAKqxa8xb9rKbCOly5baowxxhgzplkCuynzOuQT/mUrGyiqoKLiNT4VbrvfCm3/KHDUaCSxK7R9uzvDXXZGpBlA0N4j/LvuiHZ3A5NHOgZjjDHGmFphCeymzfpM7K8TGyguU0QVr7GPOL8sH9vGKD2+/1H5bTuU8ZsUrxmgkd4Vp/r5R6PdzcDykY7BGGOMMaZWWAK7aQfEJFz3Gu/R/4KWAQ+k8ZZwz31ClRF/fJ9M573LggN3FZEmd20tvUYevb1F+gJAgHZg/kjGYIwxxhhTSyyB3bRJQPdc/+p7PbQbQMVrWqntU64L57Qx8o/vD19P88QiiZigEqPc85HYFY8AE4EkcAuwYIRjMMYYY4ypGZbAbtoKoHlPr7B+hix5yG2SRhD/suCg/RjBx/fRql/vjxE2hXh+Gb+4oyy+eVdvUSfwNHAecBXz1upIxWCMMcYYU2ti1Q6gDtwB7AGsOtKbf+cvgxNerUgjIs0PaHL3K4IDHj1m5K79OmDnBilPBOjT2Irb9VWfZ97awshd0hhjjDGmtlkP7KYtwD2mT77Xv3Z1K90rBRWBlnXa0nNa6VP7jeC15/qEiThhm4IGeP8s5FKFEbyeMcYYY0zNswR2U9zj+auA8xJSLrzBu+dWRYplYmEPjarIicl0vnG4L5tM5/cF5jRKaRJASf01RWK/GO7rGGOMMcbUGyshGAqXxD4JPHl+On9ZE8VXN0gws0HKE4rqrwM5Hrh0uC4X1b5+yiOMxwk7AC3jXVvIpR4ermsYY4wxxtQr64HdTIVcqrtI7DyFwEebYoTNwAeGuRf2DcCrGilPAiiqv7ZI7PvDeH5jjDHGmLplCewWCPAuLKn/PECjG2A1EThxOM6dTOcTRL2vCQk6AELkikIu9cBwnN8YY4wxpt5ZArsFCrnUygDvXIUwRtgaI2gC5ibT+Y5hOP17ge2bpLQNICW81b3Ec8NwXmOMMcaYMcES2C3UR+zcMt4SgEYpT8atiPWJV3LOZDq/PfCBGEFTnLBdQQP1flvIpZ4ahpCNMcYYY8YES2C3UCGXWldW7wdRL2xLnKAFeGsynd9jS86XTOc9IAuaaJLSFIAAb1Ev8e8OZ9zGGGOMMfXOEthXoI/4eYo8BtAkpW1BPWBeMp1v2oLTzQX2bqA8wUebQqRUVu+MQi61bjhjNsYYY4ypd5bAvgKFXKrYq7HTQqTooYlGyhOAJHD65pwnmc6/HvioRxiPyhEQ9Npe4n8b/qiNMcYYY+qbJbCv0OO542+PEf4ZoEHKk33CBHB8Mp0/aSjtk+n8LOAcUK9FitMEPIXla7Xpo4VcSkcydmOMMcaYemQJ7DBYpc2f9tCCgDRLcRqoAJ9PpvMnbKxdMp3fDfgV0NJEabKPNimUBD5SyKVWjkbsxhhjjDH1RlStk284zPnyn/dUuEGRphL+2i6NLwYB+APw80Iu1dN/bDRg623AZ4DGBOWOZilNBWiS0jdvP/uks6twC8YYY4wxdcES2GF0+FcvPHFV2PQbRfw+9Vf2EH8+SmJXCXr1fvJY1xRZfcDjuv2cFdrR3kVjl+IlmqW0PUCL9P3tuXDce610wBhjjDFmwyyBHWZHfPV3p60IW84OEa+Iv7Zb40sA7aCro4Xe1hAvCJFQUA+R1hKJxhAvmOh1X7EgmPguS16NMcYYYzbOEtgR8M6v/eJ9hWD8D/o01hAixUBZ00FnY5FYHyAgCRWvDSSeIGC2v+yS9bR+4LKzPmTfDGOMMcaYTbAEdoR85Mzvz1katp33bNAxGzQhKAoBiAeIh7KDt2rte/1/XXOCd+OVzFt7SbVjNsYYY4ypB5bAjqBsNhtbFza8S8K+M5/TCZN7NS4NUg4nybqV+3mP3f0OueY/rXT7AMxb+6Mqh2uMMcYYUxcsgR0N8zpOXk/L7FWM622js3cCa3sq9k4EnrYeWGOMMcaYoYlVO4CtxB1tdO3RRtdSoPIdgwDtwPzqhGWMMcYYU38sgR0dC4BbgIOBdUA30IxLXm+J9htjjDHGmCGwEoLRMq9DgFnA/sBkYDmu53UB89baN8EYY4wxZogsgTXGGGOMMXXFq3YAxhhjjDHGbA5LYI0xxhhjTF2xBNYYY4wxxtQVS2CNMcYYY0xdsQTWGGOMMcbUFUtgjTHGGGNMXbEE1hhjjDHG1BVLYI0xxhhjTF2xBNYYY4wxxtQVS2CNMcYYY0xdsQTWGGOMMcbUFUtgjTHGGGNMXbEE1hhjjDHG1BVLYI0xxhhjTF2xBNYYY4wxxtQVS2CNMcYYY0xdsQTWGGOMMcbUFUtgjTHGGGNMXbEE1hhjjDHG1BVLYI0xxhhjTF2xBNYYY4wxxtQVS2CNMcYYY0xdsQTWGGOMMcbUFUtgjTHGGGNMXbEE1hhjjDHG1BVLYI0xxhhjTF2xBNYYY4wxxtQVS2CNMcYYY0xdsQTWGGOMMcbUFUtgjTHGGGNMXbEE1hhjjDHG1BVLYI0xxhhjTF2xBNYYY4wxxtQVS2CNMcYYY0xdsQTWGGOMMcbUFUtgjTHGGGNMXbEE1hhjjDHG1BVLYI0xxhhjTF35f5Zvmp3PhXNuAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 576x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x_physics = torch.linspace(0,1,30).view(-1,1).requires_grad_(True)# sample locations over the problem domain\n",
    "mu, k = 2*d, w0**2\n",
    "\n",
    "torch.manual_seed(123)\n",
    "model = FCN(1,1,32,3)\n",
    "optimizer = torch.optim.Adam(model.parameters(),lr=1e-4)\n",
    "files = []\n",
    "for i in range(20000):\n",
    "    optimizer.zero_grad()\n",
    "    \n",
    "    # compute the \"data loss\"\n",
    "    yh = model(x_data)\n",
    "    loss1 = torch.mean((yh-y_data)**2)# use mean squared error\n",
    "    \n",
    "    # compute the \"physics loss\"\n",
    "    yhp = model(x_physics)\n",
    "    dx  = torch.autograd.grad(yhp, x_physics, torch.ones_like(yhp), create_graph=True)[0]# computes dy/dx\n",
    "    dx2 = torch.autograd.grad(dx,  x_physics, torch.ones_like(dx),  create_graph=True)[0]# computes d^2y/dx^2\n",
    "    physics = dx2 + mu*dx + k*yhp# computes the residual of the 1D harmonic oscillator differential equation\n",
    "    loss2 = (1e-4)*torch.mean(physics**2)\n",
    "    \n",
    "    # backpropagate joint loss\n",
    "    loss = loss1 + loss2# add two loss terms together\n",
    "    loss.backward()\n",
    "    optimizer.step()\n",
    "    \n",
    "    \n",
    "    # plot the result as training progresses\n",
    "    if (i+1) % 150 == 0: \n",
    "        \n",
    "        yh = model(x).detach()\n",
    "        xp = x_physics.detach()\n",
    "        \n",
    "        plot_result(x,y,x_data,y_data,yh,xp)\n",
    "        \n",
    "        file = \"plots/pinn_%.8i.png\"%(i+1)\n",
    "        plt.savefig(file, bbox_inches='tight', pad_inches=0.1, dpi=100, facecolor=\"white\")\n",
    "        files.append(file)\n",
    "        \n",
    "        if (i+1) % 6000 == 0: plt.show()\n",
    "        else: plt.close(\"all\")\n",
    "            \n",
    "save_gif_PIL(\"pinn.gif\", files, fps=20, loop=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "7026fd49",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
